صورة الغلاف

Gauge invariant degeneracies and rotational symmetry eigenstates in noncommutative plane

We calculate the gauge invariant energy eigenvalues and degeneracies of a spinless charged particle confined in a circular harmonic potential under the influence of a perpendicular magnetic field B on a 2D noncommutative plane. The phase space coordinates transformation based on the 2-parameter fami...

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التفاصيل البيبلوغرافية
المؤلفون الرئيسيون: M. Rusli, M. N. N., M. S., Nurisya, Zainuddin, H., Umar, M. F., Ahmed Jellal, .
التنسيق: مقال
منشور في: Damghan University 2022
الوصول للمادة أونلاين:http://psasir.upm.edu.my/id/eprint/101601/
https://jhap.du.ac.ir/article_281.html
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spelling my.upm.eprints.1016012024-04-22T04:14:21Z http://psasir.upm.edu.my/id/eprint/101601/ Gauge invariant degeneracies and rotational symmetry eigenstates in noncommutative plane M. Rusli, M. N. N. M. S., Nurisya Zainuddin, H. Umar, M. F. Ahmed Jellal, . We calculate the gauge invariant energy eigenvalues and degeneracies of a spinless charged particle confined in a circular harmonic potential under the influence of a perpendicular magnetic field B on a 2D noncommutative plane. The phase space coordinates transformation based on the 2-parameter family of unitarily equivalent irreducible representations of the nilpotent Lie group GNC was used to accomplish this. We find that the energy eigenvalues and quantum states of the system are unique since they depend on the particle of interest and the applied magnetic field $B$. Without B, we essentially have a noncommutative planar harmonic oscillator under the Bopp shift formulation. The corresponding degeneracy is not unique with respect to the choice of particle, and they are only reliant on the two free integral parameters. The degeneracy is not unique for the scale Bθ = h and is in fact isomorphic to the Landau problem in symmetric gauge; thus, each energy level is infinitely degenerate for any arbitrary magnitude of magnetic field. If 0 < Bθ < h , the degeneracy is unique with respect to both the particle of interest and the applied magnetic field. The system is, in principle, highly non-degenerate and, in practice, effectively non-degenerate, as only the finely-tuned magnetic field can produce degenerate states. In addition, the degeneracy also depends on the two free integral parameters. Numerical examples are provided to present the degeneracies, probability densities, and effects of B and θ on the ground and excited states of the system for all cases using the physical constants from the numerical simulation and experiment on a single GaAs parabolic quantum dot. Damghan University 2022 Article PeerReviewed M. Rusli, M. N. N. and M. S., Nurisya and Zainuddin, H. and Umar, M. F. and Ahmed Jellal, . (2022) Gauge invariant degeneracies and rotational symmetry eigenstates in noncommutative plane. Journal of Holography Applications in Physics, 2 (4). pp. 11-36. ISSN 2783-4778; ESSN: 2783-3518 https://jhap.du.ac.ir/article_281.html 10.22128/JHAP.2022.584.1032
institution Universiti Putra Malaysia
building UPM Library
collection Institutional Repository
continent Asia
country Malaysia
content_provider Universiti Putra Malaysia
content_source UPM Institutional Repository
url_provider http://psasir.upm.edu.my/
description We calculate the gauge invariant energy eigenvalues and degeneracies of a spinless charged particle confined in a circular harmonic potential under the influence of a perpendicular magnetic field B on a 2D noncommutative plane. The phase space coordinates transformation based on the 2-parameter family of unitarily equivalent irreducible representations of the nilpotent Lie group GNC was used to accomplish this. We find that the energy eigenvalues and quantum states of the system are unique since they depend on the particle of interest and the applied magnetic field $B$. Without B, we essentially have a noncommutative planar harmonic oscillator under the Bopp shift formulation. The corresponding degeneracy is not unique with respect to the choice of particle, and they are only reliant on the two free integral parameters. The degeneracy is not unique for the scale Bθ = h and is in fact isomorphic to the Landau problem in symmetric gauge; thus, each energy level is infinitely degenerate for any arbitrary magnitude of magnetic field. If 0 < Bθ < h , the degeneracy is unique with respect to both the particle of interest and the applied magnetic field. The system is, in principle, highly non-degenerate and, in practice, effectively non-degenerate, as only the finely-tuned magnetic field can produce degenerate states. In addition, the degeneracy also depends on the two free integral parameters. Numerical examples are provided to present the degeneracies, probability densities, and effects of B and θ on the ground and excited states of the system for all cases using the physical constants from the numerical simulation and experiment on a single GaAs parabolic quantum dot.
format Article
author M. Rusli, M. N. N.
M. S., Nurisya
Zainuddin, H.
Umar, M. F.
Ahmed Jellal, .
spellingShingle M. Rusli, M. N. N.
M. S., Nurisya
Zainuddin, H.
Umar, M. F.
Ahmed Jellal, .
Gauge invariant degeneracies and rotational symmetry eigenstates in noncommutative plane
author_facet M. Rusli, M. N. N.
M. S., Nurisya
Zainuddin, H.
Umar, M. F.
Ahmed Jellal, .
author_sort M. Rusli, M. N. N.
title Gauge invariant degeneracies and rotational symmetry eigenstates in noncommutative plane
title_short Gauge invariant degeneracies and rotational symmetry eigenstates in noncommutative plane
title_full Gauge invariant degeneracies and rotational symmetry eigenstates in noncommutative plane
title_fullStr Gauge invariant degeneracies and rotational symmetry eigenstates in noncommutative plane
title_full_unstemmed Gauge invariant degeneracies and rotational symmetry eigenstates in noncommutative plane
title_sort gauge invariant degeneracies and rotational symmetry eigenstates in noncommutative plane
publisher Damghan University
publishDate 2022
url http://psasir.upm.edu.my/id/eprint/101601/
https://jhap.du.ac.ir/article_281.html
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score 13.251813

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